Magnitude of external electric force on electric dipole

AI Thread Summary
The magnitude of the total electric force on an electric dipole is zero because the two opposing electric force vectors cancel each other out. The total electric force vector is the zero vector, leading to a magnitude of zero. While the sum of the magnitudes of the forces on each side of the dipole could be calculated as 2qE, this value lacks physical significance in this context. The discussion emphasizes that the absolute values must be calculated correctly, as they do not equate to the sum of the magnitudes. A net force can exist on a dipole only if the electric field varies across different points.
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Homework Statement
Please see below
Relevant Equations
Torque = electric dipole moment x electric field strength
For this part(b) of this problem, how is the magnitude of the total electric force zero?
1670732643570.png

I thought it would be:
1670732728637.png

If they asked for the total electric force, then I would have said zero because the two electric force vectors cancel.

Many thanks!
 

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Callumnc1 said:
For this part(b) of this problem, how is the magnitude of the total electric force zero?

I thought it would be:
View attachment 318599
What is the value of ##-qE + qE##? What is the value of ##|-qE + qE|##?

Callumnc1 said:
If they asked for the total electric force, then I would have said zero because the two electric force vectors cancel.
Yes, the total electric force vector is the zero vector. So, the magnitude of the total electric force is the magnitude of the zero vector.

If they had asked for the sum of the magnitudes of the two forces, then you would get ##2qE##. But this doesn't have much physical significance. The sum of the magnitudes of two vectors is generally not the same as the magnitude of the sum of the two vectors.
 
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TSny said:
What is the value of ##-qE + qE##? What is the value of ##|-qE + qE|##?Yes, the total electric force vector is the zero vector. So, the magnitude of the total electric force is the magnitude of the zero vector.

If they had asked for the sum of the magnitudes of the two forces, then you would get ##2qE##. But this doesn't have much physical significance. The sum of the magnitudes of two vectors is generally not the same as the magnitude of the sum of the two vectors.
Thanks for your help @TSny! The value of
1670738654075.png
is zero. And the value of
1670738677513.png
is 2qE, correct?

Many thanks!
 
Orodruin said:
Wrong. The difference is taken before the magnitude.
Ok thank you for pointing that out @Orodruin !
 
You could also have sorted this out if you kept in mind that force is a vector which has magnitude and direction. Both are needed to specify a vector. In this case, if the force on the dipole were ##2qE##, what would its direction be and why?
 
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kuruman said:
You could also have sorted this out if you kept in mind that force is a vector which has magnitude and direction. Both are needed to specify a vector. In this case, if the force on the dipole were ##2qE##, what would its direction be and why?
Thanks for your reply @kuruman ! Is it not impossible for the force on the dipole to be 2qE since the charges are equal and opposite?

Many thanks,
Callum
 
It is impossible for the force on the dipole to be 2qE. I was referring to this statement in post #1 where you seem to think that it is 2qE. Did I miss your point? What did you think would be 2qE?

Callumnc1 said:
I thought it would be:
View attachment 318599
If they asked for the total electric force, then I would have said zero because the two electric force vectors cancel.
 
Thanks for your reply @kuruman! I though the magnitude of the force was 2qE because I though
1670811188103.png
. But apparently absolute values bars don't work like that.

I guess 2qE would be the magnitude of the external electric force on each side of the dipole added together, correct?

Many thanks!
 
  • #10
Callumnc1 said:
apparently absolute values bars don't work like that.
They could not work like that. The bars mean "take the absolute value of what is between the bars". What is between the bars is -qE+qE, which is zero.
Likewise ##(x+y)^2## is not the same as ##(x^2+y^2)##.
 
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  • #11
Callumnc1 said:
apparently absolute values bars don't work like that.
The bars are like parentheses except, after you calculate what's between them, you strip the negative sign if it's there.

Example
##|5-2|=|3|=3##

##|2-5|=|-3|=3.##
 
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  • #12
  • #13
If the net charge is zero, the net force (and hence its magnitude) can only be non-zero if the electric field is not constant. You can however have a net force on a dipole if the field is different in different points.
 
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  • #14
Orodruin said:
If the net charge is zero, the net force (and hence its magnitude) can only be non-zero if the electric field is not constant. You can however have a net force on a dipole if the field is different in different points.
Thank you @Orodruin !
 
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